from manim import *
class math(MovingCameraScene):
    def construct(self):
        self.camera.background_color = BLACK  # 设置背景颜色
        self.camera.frame_width = 100  # 设置边框宽度
        self.camera.frame_height = 60  # 设置边框高度
        self.camera.pixel_height = 1080  # 设置像素高度
        self.camera.pixel_width = 1920  # 设置像素宽度
        self.camera.center = ORIGIN  # 设置中心点位置
        self.camera.scale_factor = 1.0  # 设置缩放因子
        #设置横线
        for i in range(60*2+1):       
            dot1=Dot([-500,5*(i-60),0]).set_opacity(0.5)
            dot2=Dot([500,5*(i-60),0]).set_opacity(0.5)
            if i==6:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
                
            else:
                line1=Line(dot1,dot2).set_color(WHITE).set_opacity(0.5)
               
            self.add(dot1,dot2,line1)
        #设置竖线
        for i in range(100*2+1):        
            dot3=Dot([(i-100)*5,-300,0]).set_opacity(0.5)
            dot4=Dot([(i-100)*5,300,0]).set_opacity(0.5)
            if i==10:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
                
            else:
                line2=Line(dot3,dot4).set_color(WHITE).set_opacity(0.5)
            self.add(dot3,dot4,line2)
        #设置三个点
        dot1 = Dot(radius=1, color=RED)  
        dot1.move_to([-47.5,27.5,0]) 
        dot2 = Dot(radius=1, color=YELLOW)  
        dot2.move_to([-42.5,27.5,0])  
        dot3 = Dot(radius=1, color=GREEN)  
        dot3.move_to([-37.5,27.5,0])
        #镜头跟进效果 
        self.camera.frame.save_state()
        #题目出现
        text0 = Tex(r"\text{(2023)}",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-37.5,2.5,0])
        text = Tex(r"\text{设函数}$f\left( x\right) $\text{在}$\left[ -a,a\right] $\text{上有二阶连续导数,证明：}"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-7,2.5,0])
       
        

        text1 = Tex(r"\text{(I)若}$f\left( 0\right) = 0,$\text{则存在}$\xi \in \left( -a,a\right) ,$\text{使得}$f''\left( \xi \right) =\dfrac{1}{a^{2}}\left[ f\left( a\right) +f\left( -a\right) \right] $"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,-2.5,0])
        text2 = Tex(r"\text{(II)若}$f\left( x\right)$\text{在}$\left( -a,a\right) $\text{内取到极值,则存在}"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-26,-7.5,0])
        text20 = Tex(r"$\eta \in \left( -a,a\right) $\text{使得}$\left| f''\left( \eta \right) \right| \geq \dfrac{1}{2a^{2}}\left| f\left( a\right) -f\left( -a\right) \right| $"
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([23,-7.5,0])
        self.play(Write(text0),Write(text),Write(text1),Write(text2),Write(text20),self.camera.frame.animate.scale(0.8))
        self.wait()
        #镜头拉回
          #分析文本
        #text100=MarkupText("<b><i>分析/解：</i></b>",color=PINK).scale(5.0).move_to([-38,12.5,0])
        self.play(Restore(self.camera.frame))
        self.play(FadeIn(dot1),run_time=0.1)
        self.play(FadeIn(dot2),run_time=0.1)
        self.play(FadeIn(dot3),run_time=0.1)
        #题目向上移动
        self.play(text0.animate().move_to([-37.5,22.5,0]),text.animate().move_to([-7,22.5,0]),text1.animate().move_to([-10,17.5,0]) ,text2.animate().move_to([-26,12.5,0]) ,text20.animate().move_to([23,12.5,0])   )

        rectangle=Rectangle(color=BLUE,fill_opacity=0.3,width=16,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle.move_to([3, 22.5, 0])
        self.play(Create(rectangle))
        text3 = Tex(r"\text{泰勒展开}",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(rectangle,UP,buff=1)
        self.play(Write(text3))

        rectangle1=Rectangle(color=GREEN,fill_opacity=0.3,width=12,height=5
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle1.move_to([-37, 17.5, 0])
        rectangle2=Rectangle(color=GREEN,fill_opacity=0.3,width=5,height=5
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle2.move_to([13.5, 17.5, 0])
        rectangle3=Rectangle(color=GREEN,fill_opacity=0.3,width=6,height=5
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle3.move_to([24, 17.5, 0])
        self.play(Create(rectangle1),Create(rectangle2),Create(rectangle3))


        text4 = Tex(r"\text{中点在端点处展开}",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,2.5,0])
        text5 = Tex(r"\text{端点在中点处展开}",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-2.5,0])
        self.play(Write(text4),Write(text5),FadeOut(rectangle3,rectangle2,rectangle1,rectangle,text3))

        rectangle4=Rectangle(color=GREEN,fill_opacity=0.3,width=32.5,height=6
                            ,stroke_color=GREEN,stroke_width=20)
        rectangle4.move_to([12.5, 17.5, 0])
        self.play(Create(rectangle4))
        rectangle5=Rectangle(color=GREEN,fill_opacity=0.0,width=32.5,height=6
                            ,stroke_color=RED,stroke_width=20)
        rectangle5.move_to([0,-2.5,0])
        self.play(Create(rectangle5),FadeOut(rectangle4))

        text6 = Tex(r"$f\left( a\right) =f\left( 0\right) +f'\left( 0\right) \left( a-0\right) +\dfrac{f''\left( \xi_1 \right) }{2!}\left( a-0\right) ^{2}$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,3,0])
        text7 = Tex(r"$f\left( -a\right) =f\left( 0\right) +f'\left( 0\right) \left( -a-0\right) +\dfrac{f''\left( \xi_2 \right) }{2!}\left( -a-0\right) ^{2}$",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-4,0])

        self.play(FadeOut(text4),ReplacementTransform(rectangle5,text6),ReplacementTransform(text5,text7))
        self.wait(0.2)



        rectangle6=Rectangle(color=BLUE,fill_opacity=0.3,width=15,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle6.move_to([-2,3, 0])
        rectangle7=Rectangle(color=BLUE,fill_opacity=0.3,width=16,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle7.move_to([-2,-4,0])
        self.play(Create(rectangle7),Create(rectangle6))

        text8 = Tex(r"$f\left( a\right) +f\left( -a\right) =\dfrac{a^{2}}{2}\left[ f''\left( \xi _{1}\right) +f''\left( \xi _{2}\right) \right] $",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([-10,0,0])
        self.play(FadeOut(rectangle6,rectangle7),ReplacementTransform(text7,text8),ReplacementTransform(text6,text8))
        self.wait(0.2)

        rectangle8=Rectangle(color=BLUE,fill_opacity=0.3,width=16,height=5
                            ,stroke_color=BLUE,stroke_width=20)
        rectangle8.move_to([3,22.5,0])
        self.play(Create(rectangle8))
        text9 = Tex(r"$f''\left( \xi _{1}\right) +f''\left( \xi _{2}\right) =2f''\left( \xi \right) $\text{,其中}$\xi \in \left( \xi _{1},\xi _{2}\right) \subset \left( -a,a\right) $",color=YELLOW
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,6,0])
        text10 = Tex(r"$=a^{2}f''\left( \xi \right) $",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).next_to(text8,RIGHT,buff=1)
        self.play(Write(text9),FadeOut(rectangle8),Write(text10),)
        text11 = Tex(r"$f''\left( \xi \right) =\dfrac{1}{a^{2}}\left[ f\left( a\right) +f\left( -a\right) \right] $",color=WHITE
                  
                   ,tex_template=TexTemplateLibrary.ctex).scale(5.0).move_to([0,-6,0])
        
        self.play(Write(text11))

        self.wait()